Is there a legitimate reason to stop cleaning up after yourself as a fully grown human adult man?
If she doesn't put out, he can boycott by no longer cleaning up after himself?
If she doesn't appreciate his "help" he can boycott by no longer cleaning up after himself?
If she micromanages his "help" he can boycott by no longer cleaning up after himself?
If she demands him to "help" on her schedule he can boycott by no longer cleaning up after himself?
You think these are all credible reasons to stop doing what any full grown human should do every day simply because they are an autonomous adult?
Yikes.
The way you use the word "help" here makes it clear that your belief is it's HER job and he's only HELPING with her job, which in your mind creates reasonable scenarios in which he would no longer be required to help her with her job.
You might want to check your own internalized misogyny.